The long-term goal of this project is to characterize the cognitive mechanisms underlying number processing and calculation, and the ways in which these mechanisms break down as a consequence of brain damage. The proposed research has two specific aims. The first is to test the hypotheses embodied in a model that analyzes the cognitive number-processing/calculation system into several functional components, and interprets the principal forms of number comprehension, number production, and calculation impairment that are observed in brain-damaged patients. The second aim is to characterize in detail the internal structure of several of the processing components postulated by the model, thereby providing a basis for a more fine-grained analysis of the wide variety of specific patterns of impaired number-processing and calculation performance that occur consequent to brain damage. These aims will be accomplished through a two-phase program of research. In the first phase a large number of patients with single focal lesions will be tested with a Dyscalculia Test Battery, to determine whether the observed patterns of impairment conform to those predicted by the proposed model. In the second phase, subgroups of patients with selective impairments to particular processing components (e.g., verbal number comprehension deficit) will be tested with sets of experimental tasks designed to probe in considerable detail the nature of the impairments. The goal in this phase is to develop detailed models of the functioning and dissolution of the major number-processing/calculation components, by bringing to bear, for each component, data from several patients with various forms of damage to that component. The computational modeling techniques of cognitive science and computational neuroscience will be employed to formulate models in computationally explicit terms. Finally, the theoretically- grounded characterizations of impairments emerging from the studies, in conjunction with lesion localization data, will be used to explore correlations between locus of lesion and type of number- processing/calculation impairment, with the aim of shedding light on relationships between cognitive and brain mechanisms in number processing and calculation. The results of the proposed studies will contribute to an understanding of number processing, calculation, and dyscalculia, and could potentially provide a foundation for development of diagnostic tests and remediation programs. The findings will also have relevance for issues extending beyond the number domain, including issues of lexical representation and processing, and general issues concerning the ways in which cognitive systems may be disrupted by brain damage.